Global gradient estimates for general nonlinear elliptic measure data problems with Orlicz growth

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We provide an optimal global Calderón-Zygmund theory for gradients of SOLAs to general nonlinear elliptic equations −divA(x,u,Du)=μ whose principle part depends on the solution itself and right-hand data μ is a signed Radon measure. The associated nonlinearity A is assumed to satisfy the (δ,R0)-BMO condition in x, local uniform continuity in u, and Orlicz growth condition in Du, while the boundary of underlying domain is assumed to be Reifenberg flat. This is achieved by employing a perturbation method together with developing a one-parameter technique and by applying the maximal function free technique.